Home
Class 12
PHYSICS
A bullet of mass m moving with a velocit...

A bullet of mass `m` moving with a velocity of `u` just grazes the top of a solid cylinder of mass `M` and radius `R` resting on a rough horizontal surface as shown and is embedded in the cylinder after impact. Assuming that the cylinder rolls without slipping, find the angular velocity of the cylinder and the final velocity of the bullet.

Text Solution

Verified by Experts

Let v and be the velocity of bullet and angular velocity of cylinder respectively. Applying conservation of angular moment about the point of contact of cylinder with floor,`m u.2R=m u.2R+(I_(CM)+MR^2)omega` Here, `v=2RomegaandI_(CM)=1/2MR_2`Substituting and solving, we get `v=(8m u)/(8m+3M) and omega =(4m u)/((83+3M)R^dot`.
Promotional Banner

Similar Questions

Explore conceptually related problems

A solid cylinder of mass M and radius R rolls without slipping on a flat horizontal surface. Its moment of inertia about the line of contact is ?

A homogeneous cylinder of mass Mand radius r is pulled on a horizontal plane by a horizontal force F acting through its centre of mass. Assuming rolling without slipping, find the angular acceleration of the cylinder,

A uniform solid cylinder of mass m and radius R is placed on a rough horizontal surface. A horizontal constant force F is applied at the top point P of the cylinder so that it start pure rolling. The acceleration of the cylinder is

A cylinder of mass m and radius R is kept on a rough surface after giving its centre a horizontal speed v_(0) . Find the speed of the centre of the cylinder when it stops slipping.

A bullet of mass m moving with velocity v strikes and becomes embedded at the edge of a cylinder of mass M and radius R_(0) as shown in fig. The cylinder, initially at rest, begins to rotate about its symmetry axis, which remains fixed in position. Assuming no frictional torque, what is the angular velocity of the cylinder after this collision? Kinetic energy conseved?

A uniform solid cylinder having mass M and radius R is pulled by a horiozntal force F acting through the center as shown. The cylinder rolls to the right without slipping. What is the magnitude of the force of friction between the cylinder and the ground?

On an uniform cylinder of mass m and radius R a constant horizontal force F is applied at any point. Choose the correct alternative if cylinder is rolling without slipping in rightward direction